How To Evaluate a Logarithm Without a Calculator with a Fraction as the Base

The video tutorial explains how to evaluate the logarithm of 16 with base 1/2 without using a calculator. It begins by introducing the problem and rewriting it in exponential form. The instructor then demonstrates how to rewrite the bases to be the same, using the properties of exponents. By applying the one-to-one property, the exponents are equated, leading to the solution that log base 1/2 of 16 equals -4. The tutorial concludes with a summary of the steps taken to solve the problem.

What is the first step in solving a logarithmic expression like log base 1/2 of 16?

• Convert it to a fraction

• Use a calculator

• Rewrite it as an equation

• Guess the answer

How can 1/2 be expressed in terms of base 2?

• 2 to the power of -1

• 2 to the power of 2

• 2 to the power of 0

• 2 to the power of 1

What is the value of 2 raised to the 4th power?

• 8

• 4

• 16

• 32

What property allows us to equate the exponents when the bases are the same?

• Commutative Property

• One-to-One Property

• Associative Property

• Distributive Property

What is the final solution for log base 1/2 of 16?

• -2

• -3

• -4

• -5